There are many reasons why national political conventions have become so clichéd and boring. The central one is this: they’re all about preaching to the converted. Even Clint Eastwood’s infamously unscripted twelve minutes required a silent opponent.

Yes, it’s true each nominee has to speak not only to the crowds in the hall but also to a vast television audience with many undecided voters. But in no sense does a nominee ever truly have to engage the ideas and arguments of the other party.

What if each nominee had to speak at the other’s convention for one night—Mitt Romney before an arena full of Democrats, or President Obama to a stadium of GOPers. How would they make their case and acknowledge the counterarguments? And how would the hostile audiences behave? Would the candidate mix it up with critics, as Lincoln and Douglas had to? Forget Clint — this would be good TV.

When we imagine what each candidate might say to the gathered opposition, we quickly realize how empty our public “debate” really is (including the presidential debates, which are more about delivering pre-cooked zingers than reckoning with the opponent’s worldview).

Had Obama been in Tampa he could’ve said something like this: “As Republicans, you believe in getting rewarded for hard work. But these days, from Wall Street to the lobbies of Washington, the game is rigged to benefit just a few folks no matter how hard everyone works. That’s not free enterprise. That’s crony capitalism. I want more freedom and competition — as you do. We’ve got to make the insiders at banks and big corporations play by the same rules as you and me.”

And if Romney were appearing in Charlotte, maybe he’d say this: “A president has to lead the country to face hard facts. The fact is, today’s Medicare is unsustainable. If you are proud of being the party that made Medicare, then help mend it now. Paul Ryan and I offer a solution that puts more decision-making in the hands of the people. If as Democrats you hate our plan, then as Americans you should offer something better — something more than scaring seniors.”

Granted, it would take a very rare set of circumstances for a president and challenger ever to agree to engage this way. But nothing stops us citizens from doing it. These days, we tend to talk politics with birds of our own ideological feather. We post snarky items to Facebook so the like-minded can ‘like’ our opinions. Perhaps if we sought out people who would actually disagree with us—if we spoke at meetings of the opposition—it would force us to get beyond tired talking points and tap into the other side’s moral and political motivations. It would make us sharpen our arguments. It would require us to listen.

In this spirit, a left-right team of grassroots activists has launched a project called Living Room Conversations where progressive and conservative guests meet to discuss polarizing topics like climate change. Of course, whether in a living room or a convention center, consensus won’t magically materialize from such encounters. Facing those with whom we differ isn’t sufficient to make democracy work. But it is necessary. And it helps us remember that our job as citizens isn’t to shout in echo chambers. It’s to engage, and perhaps, to persuade, so that even if we can’t win converts we can at least earn respect—simply for showing up.